Question: Solve for $x$ and $y$ using substitution. ${-x+y = -2}$ ${y = 5x+2}$
Answer: Since $y$ has already been solved for, substitute $5x+2$ for $y$ in the first equation. ${-x + }{(5x+2)}{= -2}$ Simplify and solve for $x$ $-x+5x + 2 = -2$ $4x+2 = -2$ $4x+2{-2} = -2{-2}$ $4x = -4$ $\dfrac{4x}{{4}} = \dfrac{-4}{{4}}$ ${x = -1}$ Now that you know ${x = -1}$ , plug it back into $\thinspace {y = 5x+2}\thinspace$ to find $y$ ${y = 5}{(-1)}{ + 2}$ $y = -5 + 2$ $y = -3$ You can also plug ${x = -1}$ into $\thinspace {-x+y = -2}\thinspace$ and get the same answer for $y$ : ${-}{(-1)}{ + y = -2}$ ${y = -3}$